text: Up to here, an ideal surface was considered, but going beyond the idealized case there are several effects which influence premelting:
  *Curvature: When the surface considered is not planar but exhibits a curvature premelting is affected. The rule is that whenever the surface is concave, viewed from the solid's perspective, then premelting is advanced. The fraction by which the thickness of the liquid film increases is given by , where r is the local radius of the curved surface. Therefore, it is also plausible that premelting starts in scratches or in corners of steps and hence has a flattening effect.
  *Disordered solids: As disorder in the solid increases its local free energy, the local chemical potential of the disordered solid lies above the chemical potential of the ordered solid. In thermodynamic equilibrium the chemical potential of the premelted liquid film has to be equal to that of the disordered solid, so it can be concluded that disorder in the solid phase causes the effect of premelting to increase.
  *Impurities: Consider the case of the depression of the ice melting temperature due to dissolved salt. For premelting the situation is far more difficult than one would expect from that simple statement. It starts with the Lifshitz theory which was roughly sketched above. But now the impurities cause screening in the liquid, they adsorb on the border between solid and liquid phase and all those effects make a general derivation of impurity effects impossible to state here. But it can be said that impurities have a great effect on the temperature from which on premelting can be observed and they especially affect the thickness of the layer. This however does not mean that the thickness is a monotone function in the concentration.